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| Codeforces Round 952 (Div. 4) |
|---|
| Finished |
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- Custom test
C. Good Prefixes
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Alex thinks some array is good if there exists some element that can be represented as the sum of all other elements (the sum of all other elements is $$$0$$$ if there are no other elements). For example, the array $$$[1,6,3,2]$$$ is good since $$$1+3+2=6$$$. Furthermore, the array $$$[0]$$$ is also good. However, the arrays $$$[1,2,3,4]$$$ and $$$[1]$$$ are not good.
Alex has an array $$$a_1,a_2,\ldots,a_n$$$. Help him count the number of good non-empty prefixes of the array $$$a$$$. In other words, count the number of integers $$$i$$$ ($$$1 \le i \le n$$$) such that the length $$$i$$$ prefix (i.e. $$$a_1,a_2,\ldots,a_i$$$) is good.
Input
The first line of the input contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases.
The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of elements in the array.
The second line of each test case contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$0 \le a_i \le 10^9$$$) — the elements of the array.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
Output
For each test case, output a single integer — the number of good non-empty prefixes of the array $$$a$$$.
Example
Input
7
1
1
1
4
1 1 2 0
5
0 1 2 1 4
7
1 1 0 3 5 2 12
7
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 294967296
10
0 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 589934592
Output
1033412
Note
In the fourth test case, the array has five prefixes:
- prefix $$$[0]$$$ is a good array, as mentioned in the statement;
- prefix $$$[0, 1]$$$ is not a good array, since $$$0 \ne 1$$$;
- prefix $$$[0, 1, 2]$$$ is not a good array, since $$$0 \ne 1 + 2$$$, $$$1 \ne 0 + 2$$$ and $$$2 \ne 0 + 1$$$;
- prefix $$$[0, 1, 2, 1]$$$ is a good array, since $$$2 = 0 + 1 + 1$$$;
- prefix $$$[0, 1, 2, 1, 4]$$$ is a good array, since $$$4 = 0 + 1 + 2 + 1$$$.
As you can see, three of them are good, so the answer is $$$3$$$.
"); $(this).append($copy); const clipboard = new Clipboard('#' + cpyId, { text: function (trigger) { const pre = document.querySelector('#' + preId); const lines = pre.querySelectorAll(".test-example-line"); return Codeforces.filterClipboardText(pre.innerText, lines.length); } }); const isInput = $(this).parent().hasClass("input"); clipboard.on('success', function (e) { if (isInput) { Codeforces.showMessage("The example input has been copied into the clipboard"); } else { Codeforces.showMessage("The example output has been copied into the clipboard"); } e.clearSelection(); }); }); $(".test-form-item input").change(function () { addPendingSubmissionMessage($($(this).closest("form")), "You changed the answer, do not forget to submit it if you want to save the changes"); const index = $(this).closest(".problemindexholder").attr("problemindex"); let test = ""; $(this).closest("form input").each(function () { const test_ = $(this).attr("name"); if (test_ && test_.substring(0, 4) === "test") { test = test_; } }); if (index.length > 0 && test.length > 0) { const indexTest = index + "::" + test; window.changedTests.add(indexTest); } }); $(window).on('beforeunload', function () { if (window.changedTests.size > 0) { return 'Dialog text here'; } }); autosize($('.test-explanation textarea')); $(".test-example-line").hover(function() { $(this).attr("class").split(" ").forEach((clazz) => { if (clazz.substr(0, "test-example-line-".length) === "test-example-line-") { let end = clazz.substr("test-example-line-".length); if (end !== "even" && end !== "odd" && end !== "0") { let top = 1E20; let left = 1E20; let problem = $(this).closest(".problemindexholder"); $(this).closest(".input").find("." + clazz).css("background-color", "#FFFDE7").each(function() { top = Math.min(top, $(this).offset().top); left = Math.min(left, $(this).offset().left); }); let testCaseMarker = problem.find(".testCaseMarker_" + end); if (testCaseMarker.length === 0) { const html = "
"; problem.append($(html)); testCaseMarker = problem.find(".testCaseMarker_" + end); } if (testCaseMarker) { testCaseMarker.show() .offset({top, left: left - 20}) .text(end); } } } }); }, function() { $(this).attr("class").split(" ").forEach((clazz) => { if (clazz.substr(0, "test-example-line-".length) === "test-example-line-") { let end = clazz.substr("test-example-line-".length); if (end !== "even" && end !== "odd" && end !== "0") { $("." + clazz).css("background-color", ""); $(this).closest(".problemindexholder").find(".testCaseMarker_" + end).hide(); } } }); }); });
